This thesis is concerned with the relationship between arousal mechanisms, attentional processes and competitive sports performance. Theoretical interpretations of the arousal-performance relationship have traditionally followed the inverted-U hypothesis. Based on this approach, the generally accepted view in sports psychology is that high levels of arousal are detrimental to good performance. A review of the relevant psychological literature reveals the limited nature of such an approach and draws attention to alternative perspectives such as those offered by the work of Apter and that of Cox and Mackay. These more recent theoretical approaches allow more sophisticated interpretations of the individual's experience of arousal to be realised. Important here are other aspects of the individual's psychological state (cognition and emotion) as these are thought to affect his or her interpretation of arousal. Interestingly, the two theories, developed independently by Apter and by Cox and Mackay, appear consistent, one with the other, and have not previously been applied to the study of competitive sport. Several different research techniques were incorporated into a research design which used squash players of varying levels of ability to examine the various psychological factors important in their experience of and performance in competitive squash. The research techniques, some of which were innovative, proved effective indentifying the interaction of arousal and stress in relation to competitive performance. It was concluded that psychological preparation and experience (i.e. number of years, number of times per week played), along with personality characteristics and attentional strategies, contribute to success in competitive squash. Fluctuations in emotional responses characterised players whose performance was unsuccessful. By way of contrast, successful players' (i.e. successful in terms of level of ability attained, skill performance and winning games) psychological responses were more consistent. They achieved and maintained high levels of arousal both prior to and during performance. High arousal was, for successful players, accompanied by low stress and positive hedonic tone when they were subject to the demands of competitive squash games. Overall, successful players (that is skilled players in Study 2 and winners from Study 3) were highly extravert and significantly less neurotic (Eysenck) than other groups of players. Telic dominance was not a discriminating characteristic in this investigation, but successful players' attentional styles were significantly different, as defined by Nideffer's BIT and INFP subscales, to those styles or strategies employed by less capable players. Successful players generally employed psychological preparation strategies prior to and during play to a greater extent than other players. When doing so, they were more concerned with cognitive strategies, in the form of focussing and planning, than arousal modulation strategies. The present research investigation advanced knowledge about the processes involved in competitive sports, providing new and relevant information. As a result, a number of suggestions for squash coaching and player development, along with implications for cognitive intervention with sports performers, have emerged.